I agree that SMB's "solution" is flawed in a few ways... you'd have to have velcro around the entire perimiter or else bugs could crawl under the net...
I don't have my own SMB to verify my ideas against, but could you make some sort of spring-loaded wooden frame that rests inside the door "wells"? This could provide pressure up against the van for a "seal" and provide the frame to connect the screen to. The frame would also have to be collapsible for easy storage....
Another idea would be to provide your own small frame (attached to the van, perhaps just inside the line of the closed doors) onto which you could "spring" your own screen onto, via a full-size screen/net edged with elastic.... think of it like a larger-scale hair net, snapping onto a wooden picture frame. You'd just need enough of a "lip" on the frame to let the elastic grab onto it easily.
Or a combination of both ideas: Create a simple wooden frame that could be "snapped" in place inside the door "wells" of the rear doors, and then snap your giant elastic hair net over/onto the frame....
Or make your screen one solid piece, attach it to the ceiling somehow, THEN use 3 wooden members to "stretch" and secure the other edges to the van...
Just brainstorming here....